Day 4 – Polynomials review Math 2 Unit 1 Day 4 – Polynomials review

Objectives By the end of today, you will be able to… Classify polynomials Add, Subtract, and Multiply Polynomials

Vocabulary A polynomial is a monomial or the sum of monomials. The exponent of the variable in a term determines the degree of that polynomial. Ordering the terms by descending order by degree. This order demonstrates the standard form of a polynomial. P(x) = 2x³ - 5x² - 2x + 5 Leading Coefficient Constant Term Cubic Term Quadratic Term Linear Term

Standard Form of a Polynomial For example: P(x) = 2x3 – 5x2 – 2x + 5 Polynomial Standard Form Polynomial

Parts of a Polynomial P(x) = 2x3 – 5x2 – 2x + 5 Leading Coefficient: Cubic Term: Quadratic Term: Linear Term: Constant Term:

Parts of a Polynomial P(x) = 4x2 + 9x3 + 5 – 3x Leading Coefficient: Cubic Term: Quadratic Term: Linear Term: Constant Tem:

Classifying Polynomials We can classify polynomials in two ways: By the number of terms # of Terms Name Example 1 Monomial 3x 2 Binomials 2x2 + 5 3 Trinomial 2x3 + 3x + 4 4 Polynomial with 4 terms 2x3 – 4x2 + 5x + 4

Classifying Polynomials 2) By the degree of the polynomial (or the largest degree of any term of the polynomial. Degree Name Example Constant 7 1 Linear 2x + 5 2 Quadratic 2x2 3 Cubic 2x3 – 4x2 + 5x + 4 4 Quartic x4 + 3x2 5 Quintic 3x5 – 3x + 7

Classifying Polynomials Write each polynomial in standard form. Then classify it by degree AND number of terms. -7x2 + 8x5 2. x2 + 4x + 4x3 + 4 3. 4x + 3x + x2 + 5 4. 5 – 3x

Activity time!

Adding Polynomials Add only like terms! Organize the polynomials in the easiest way you can see it; (vertically/horizontally). Simplify all terms completely and totally. Make sure of the signs in front of the parenthesis. Cancel out any terms if necessary! This is an example of how to add polynomials and a good way to group them to make sure of the signs and like terms! :)

Subtracting Polynomials Set the problem up however you are comfortable; (vertically or horizontally). Remember to completely simplify the polynomials. Pay attention to the sign infront of the parenthesis and make sure to distribute it to all variables. Cancel and simplify all variables and terms in the polynomials. This is an example of subtracting horizontally! Notice the distribution of the sign to the variables!

Multiplying Polynomials Choose to set up either the polynomials horizontally or vertically; (based on preference). Keep in mind the signs in front of the variables. When multiplying the variables that contain an exponent, instead of multiplying them together add them instead. Always distribute any number, sign, or variable in front of parenthesis. This demonstrates the principle of distributing the terms in front of the parenthesis and making sure of the exponents.

CW & HW On your own sheet of paper, complete the odd numbers for class work and turn them in. They will be assessed for both completeness and accuracy so do your best! Finish the remainder of the worksheet for HW.